Abel
A137452 \(\bbox[yellow, 5px]{\color{DarkGreen} T_{n, k} \ = \ is(k = 0)\ ? \ 0^n : \binom{n-1}{k-1} (-n)^{n - k} } \)
\(T_{n, n - k}\) ➤ Trev ➤ 1 1 0 1 2 0 1 6 9 0 1 12 48 64 0 1 20
\(T_{n - k, k} \ \ (k \le n/2)\) ➤ Tantidiag ➤ 1 0 0 1 0 2 0 9 1 0 64 6 0 625 48 1 0
\(\sum_{j=0}^{k} T_{n, j}\) ➤ Tacc ➤ 1 0 1 0 2 3 0 9 15 16 0 64 112 124 125
\(T_{n + 2, n}\) ➤ TablDiag2 ➤ 0 9 48 150 360 735 1344 2268 3600 5445
\(T_{n + 3, n}\) ➤ TablDiag3 ➤ 0 64 500 2160 6860 17920 40824 84000
\(\text{lcm}_{k=0}^{n}\ | T_{n, k} |\ \ (T_{n,k}>1)\) ➤ TablLcm ➤ 1 1 2 18 192 7500 38880 7058940
\(\sum_{k=0}^{n} \sum_{j=0}^{k} T_{n, j}\) ➤ AccSum ➤ 1 1 5 40 425 5616 88837 1638400
\(\sum_{k=0}^{n/2} T_{n - k, k}\) ➤ AntiDSum ➤ 1 0 1 2 10 70 674 8288 124280 2200174
\(T_{n, n / 2}\) ➤ ColMiddle ➤ 1 0 2 9 48 500 2160 36015 143360
\(T_{2 n + 1, n}\) ➤ CentralO ➤ 0 9 500 36015 3306744 372027810
\(\sum_{k=0}^{3} T_{3, k}\ n^k\) ➤ PolyRow3 ➤ 0 16 50 108 196 320 486 700 968 1296
\(T_{n + 1, n-k} \) ➤ RevToff11 ➤ 0 2 0 6 9 0 12 48 64 0 20 150 500 625 0
\(T_{n + 1, n-k} \) ➤ RevTrev11 ➤ 0 0 2 0 9 6 0 64 48 12 0 625 500 150 20
\(T_{n - k, n - 2k} \ \ (k \le n/2)\) ➤ RevTantidiag ➤ 1 1 1 0 1 2 1 6 0 1 12 9 1 20 48 0 1 30
\(\sum_{j=0}^{n-k} T_{n, n-j}\) ➤ RevTacc ➤ 1 1 1 1 3 3 1 7 16 16 1 13 61 125 125 1
\(T_{n, n-k}\ (-1)^{n-k}\) ➤ RevTalt ➤ 1 1 0 1 -2 0 1 -6 9 0 1 -12 48 -64 0 1
\(T_{n + 1, n-k}\ (n-k + 1) \) ➤ RevTder ➤ 0 2 0 6 18 0 12 96 192 0 20 300 1500
\(\sum_{k=0}^{n} T_{n, n-k}\ [2 | k]\) ➤ RevEvenSum ➤ 1 1 1 10 49 776 6841 154400 1979713
\(\sum_{k=0}^{n} T_{n, n-k}\ (1 - [2 | k])\) ➤ RevOddSum ➤ 0 0 2 6 76 520 9966 107744 2803256
\(\sum_{k=0}^{n} \sum_{j=0}^{k} T_{n, n - j}\) ➤ RevAccRevSum ➤ 1 1 5 40 425 5616 88837 1638400
\(\sum_{k=0}^{n/2} T_{n - k, n-k}\) ➤ RevAntiDSum ➤ 1 1 1 3 7 22 69 245 903 3577 14757
\(T_{n, n / 2}\) ➤ RevColMiddle ➤ 1 1 2 6 48 150 2160 6860 143360 459270
\(T_{2 n + 1, n}\) ➤ RevCentralO ➤ 1 6 150 6860 459270 40584852 4459971516
\(\sum_{k=0}^{n} T_{n, n-k}\ (-2)^{n - k} \) ➤ RevNegHalf ➤ 1 -2 0 -2 -16 -162 -2048 -31250 -559872
\(\sum_{k=0}^{n} T_{n, n-k}\ (k + 1)\) ➤ RevTransNat1 ➤ 1 1 5 40 425 5616 88837 1638400
\(\sum_{k=0}^{n} T_{n, n-k}\ k^{2}\) ➤ RevTransSqrs ➤ 0 0 2 42 780 15120 318990 7397376
\(\sum_{k=0}^{n} T_{n, n-k}\ n^k\) ➤ RevPolyDiag ➤ 1 1 5 100 4913 456976 69343957